An everyday explanation

Percent Change Formula: Steps, Examples, and Pitfalls

WikiAnswerly AI · Updated October 11, 2026 · 5 min read

Written and checked with AI using the references below. This is not human expert review.

Quick answer

Subtract the old value from the new value, divide by the old value, then multiply by 100 to get percent change. A positive result means an increase; a negative result means a decrease. The formula requires the old value to be non-zero.

The Formula and What Each Part Means

Percent change tells you how much a value grew or shrank relative to where it started. The standard formula is:

Percent Change = ((V₂ − V₁) / V₁) × 100

V₁ = the original (old) value, always the denominator
V₂ = the new value
V₂ − V₁ = the actual change (positive if the value went up, negative if it went down)

One hard rule: V₁ cannot be zero. Division by zero is undefined, so the formula simply does not apply when the starting value is zero.

Four Steps to Calculate Percent Change

Identify V₁ and V₂. V₁ is always the earlier or reference value. V₂ is the later or comparison value.
Find the actual change. Compute V₂ − V₁. Keep the sign: a negative number means the value fell.
Divide by V₁. This scales the change relative to the starting point.
Multiply by 100. This converts the decimal ratio to a percentage.

Worked Example (Illustrative)

Suppose a house was worth $100,000 last year and is worth $110,000 today.

V₁ = $100,000 (old value)
V₂ = $110,000 (new value)
Actual change: $110,000 − $100,000 = $10,000
Divide: $10,000 / $100,000 = 0.10
Multiply: 0.10 × 100 = 10%

The house increased in value by 10%. This matches the formula result directly: (110,000 − 100,000) / 100,000 = 0.1 = 10%.

Verification Step

To check: take the old value and apply the percent change. $100,000 × (1 + 0.10) = $100,000 × 1.10 = $110,000. That equals V₂, so the calculation is correct.

For a decrease, check the same way. If a $200 item drops to $170, the percent change is (170 − 200) / 200 × 100 = −30/200 × 100 = −15%. Verification: $200 × (1 − 0.15) = $200 × 0.85 = $170. Confirmed.

Reading the Result: Positive vs. Negative

The sign of your answer tells you the direction of change right away.

Positive result: the value increased. A 10% result means the new value is 110% of the original.
Negative result: the value decreased. A result of −60% means the final amount is 40% of the original.
Zero: no change occurred.
−100%: the value dropped to zero entirely.

Results above 100% are valid. An 800% increase means the final amount is 9 times the original (100% + 800% = 900%).

Percent Change vs. Percentage Points: A Common Mistake

This is the most frequent error people make. When the value you are tracking is already a percentage, a raw subtraction gives you percentage points, not percent change.

Say a savings account interest rate rises from 3% to 4%. The absolute change is 1 percentage point (4% − 3% = 1 pp). But the percent change in the rate is:

(4% − 3%) / 3% × 100 = 1/3 × 100 ≈ 33.3%

Saying the rate “increased by 1%” is misleading. The correct statement is: the rate increased by 1 percentage point, or by about 33% relative to its previous level. This distinction matters in financial reporting, economics, and understanding how inflation is measured.

The U.S. Bureau of Labor Statistics, for example, reports the Consumer Price Index using 1-month and 12-month percent changes, not raw point differences, precisely because percent change accounts for the size of the starting value.

Watch Out: Sequential Percent Changes Do Not Add Up

A +10% change followed by a −10% change does not return you to the starting value. Here is why:

Start: $200
After +10%: $200 × 1.10 = $220
After −10%: $220 × 0.90 = $198 (not $200)

The two percent changes apply to different base values ($200 and $220), so they do not cancel. The net result is a 1% loss. Always apply each percent change to the value it actually starts from, not the original base.

This matters whenever you chain multiple changes together, such as year-over-year price adjustments or compounding discounts. For more on the order in which operations apply, see how PEMDAS governs the order of operations.

Edge Cases and When the Formula Breaks Down

Starting Value Is Zero

If V₁ = 0, the formula requires dividing by zero, which is undefined. There is no valid percent change in this situation. You can report the absolute change (V₂ − 0 = V₂) but not a percentage.

Negative Starting Values

When V₁ is negative, the formula can produce results that are counterintuitive. For example, going from −10 to −6: (−6 − (−10)) / (−10) × 100 = 4 / (−10) × 100 = −40%, which suggests a decrease even though the value moved closer to zero (and in many practical contexts, improved). Use the formula with caution for negative reference values and consider whether a different measure better fits your context.

When the Variable Is Already a Percentage

As shown above, use percentage points for the absolute difference and the percent change formula only when you specifically want the relative change in the rate itself.

Frequently asked questions

What if my starting value is negative?

The formula can give misleading results with a negative starting value. For example, going from −10 to −6 produces a negative percent change even though the number moved toward zero. The formula is most reliable when the reference value is positive. For negative starting values, consider reporting the absolute change instead.

How do I find the new value if I know the original and the percent change?

Rearrange the formula: New Value = Old Value × (1 + Percent Change / 100). For example, if a $50 item increases by 20%, the new price is $50 × 1.20 = $60. For a 15% decrease: $50 × (1 − 0.15) = $50 × 0.85 = $42.50.

Does a 100% increase mean the value doubled?

Yes. A 100% increase means the change equals the original amount, so the final value is 200% of the original, which is double. An 800% increase means the final amount is 9 times the original (100% + 800% = 900% of the starting value).

Why does a 10% increase followed by a 10% decrease not return to the original?

Each percent change applies to a different base. The 10% increase raises $200 to $220, then the 10% decrease applies to $220, removing $22, leaving $198. The two percentages reference different starting points, so they do not cancel. The net loss is 1% of the original.

When should I use percentage points instead of percent change?

Use percentage points when the value you are comparing is itself a percentage, such as an interest rate or a poll result. If a rate moves from 3% to 4%, the absolute shift is 1 percentage point. The percent change in the rate is about 33%. Mixing these up is a common error in financial and news reporting.

Sources

Consumer Price Index Frequently Asked Questions : U.S. Bureau of Labor Statistics · Bureau of Labor Statistics (bls.gov)
Relative change - Wikipedia · en.wikipedia.org
Percentage - Wikipedia · en.wikipedia.org

Written by AI; checked through automated evidence and editorial review. References retrieved October 11, 2026.

Spotted an error? Tell us what needs correcting.